Florence threw for 341 yards and four touchdowns, Mike Hicks returned a fumble for a score and Baylor beat SMU 59-24 on Sunday night in the opener for both teams.
"He just told me to be myself," Florence said. "I learned a lot from (Griffin). He's done a lot for our program. Just because he leaves, doesn't mean anything different happens here."
For at least one game, Baylor's offense didn't miss a beat with Florence in charge.
Florence last started as a freshman in 2009 when he replaced an injured Griffin for several games.
The senior was 21 of 30 and guided Baylor to 613 yards of offense Sunday. The Bears scored at least 45 points for the fifth straight game.
"I couldn't ask for a better situation to step into," said Florence, who didn't play in the fourth quarter. "The guys have a lot of confidence and there a lot of playmakers out here."
Florence threw first-half touchdown passes to Lanear Sampson, Jordan Najvar and Tevin Reese, and hooked up with Sampson on a 36-yard scoring pass that put the Bears on top 45-3 in the third before Bryce Petty took over at quarterback.
"We felt like we knew what we had," Baylor coach Art Briles said. "I think they wanted to prove themselves and they did tonight."
SMU has lost 10 consecutive games to Baylor dating to 1986 when the schools were members of the defunct Southwest Conference.
The Bears intercepted two of Gilbert's passes and held the Mustangs without a touchdown until late in the third quarter.
"I've got to play better," Gilbert said "We can't shoot ourselves in the foot the way we did."
In last season's opener, Baylor blew a 24-point lead before beating TCU 50-48 on a late field goal. The Bears didn't need any late drama this time.
SMU's Darius Johnson couldn't handle Gilbert's pass at the goal line and the ball bounced high in the air. Hicks twice tipped the ball before Lackey intercepted it and returned it 23 yards.
Three plays later, Florence hit a streaking Reese for a 50-yard TD pass that extended Baylor's lead to 21-3 with 2:02 left in the first half.
"That was the turning point of the game," Florence said.
On the opening drive of the third quarter, Johnson caught a short pass and lost the ball just before hitting the ground. Hicks picked up the loose ball and ran 66 yards for a touchdown.
Baylor has won seven in a row. Only TCU at eight, has a longer streak in the Football Bowl Subdivision.
The Bears matched a school-record last season with 10 wins, a mark that was first set during star linebacker Mike Singletary's senior season in 1980. Griffin, now with the Washington Redskins, capped his career by leading Baylor to its first bowl victory in 19 years.
Baylor's offense figured to take a step back without Griffin and four other offensive players from last year's squad taken in the NFL draft.
Instead, the Bears continued to pile up points as they did under Griffin.
"When you have the ability to explode on either side, you have the opportunity to be a good football team," Briles said.
Florence was 4 for 4 on Baylor's opening possession, which was aided by four SMU penalties. He capped the drive with a 6-yard touchdown pass to Sampson.
The senior dropped in a 32-yard pass to Levi Norwood to set up a 5-yard scoring toss to Najvar.
Gilbert was a highly touted recruit from Austin who played in the 2009 BCS title game before his career fizzled with the Longhorns. In his first start with SMU, Gilbert had three passes swatted down at the line and struggled to find receivers down the field.
Gilbert connected on five straight attempts, leading to Chase Hover's 22-yard field goal in the second quarter. The junior threw scoring passes to Der'rikk Thompson and Jeremy Johnson in the second half.